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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 63 72 6f 73 73 20 2d |\section|{cross -|
|00000010| 2d 2d 20 56 65 63 74 6f | 72 20 63 72 6f 73 73 20 |-- Vecto|r cross |
|00000020| 70 72 6f 64 75 63 74 7d | 0d 5c 6c 61 62 65 6c 7b |product}|.\label{|
|00000030| 66 6e 3a 63 72 6f 73 73 | 7d 0d 5c 69 6e 64 65 78 |fn:cross|}.\index|
|00000040| 7b 63 72 6f 73 73 28 29 | 7d 0d 5c 69 6e 64 65 78 |{cross()|}.\index|
|00000050| 7b 76 65 63 74 6f 72 20 | 63 72 6f 73 73 20 70 72 |{vector |cross pr|
|00000060| 6f 64 75 63 74 7d 0d 5c | 69 6e 64 65 78 7b 74 72 |oduct}.\|index{tr|
|00000070| 69 70 6c 65 20 70 72 6f | 64 75 63 74 7d 0d 5c 62 |iple pro|duct}.\b|
|00000080| 65 67 69 6e 7b 72 61 69 | 6c 7d 0d 43 72 6f 73 73 |egin{rai|l}.Cross|
|00000090| 20 3a 20 27 63 72 6f 73 | 73 27 20 27 28 27 20 4d | : 'cros|s' '(' M|
|000000a0| 61 74 72 69 78 20 27 2c | 27 20 4d 61 74 72 69 78 |atrix ',|' Matrix|
|000000b0| 20 27 29 27 20 3b 0d 5c | 65 6e 64 7b 72 61 69 6c | ')' ;.\|end{rail|
|000000c0| 7d 0d 0d 5c 76 65 72 62 | 2b 63 72 6f 73 73 2b 20 |}..\verb|+cross+ |
|000000d0| 63 61 6c 63 75 6c 61 74 | 65 73 20 74 68 65 20 76 |calculat|es the v|
|000000e0| 65 63 74 6f 72 20 63 72 | 6f 73 73 20 70 72 6f 64 |ector cr|oss prod|
|000000f0| 75 63 74 20 6f 66 20 74 | 68 65 20 74 77 6f 0d 61 |uct of t|he two.a|
|00000100| 72 67 75 6d 65 6e 74 20 | 6d 61 74 72 69 63 65 73 |rgument |matrices|
|00000110| 2e 20 20 42 6f 74 68 20 | 61 72 67 75 6d 65 6e 74 |.  Both |argument|
|00000120| 73 20 6d 75 73 74 20 68 | 61 76 65 20 74 68 72 65 |s must h|ave thre|
|00000130| 65 20 65 6c 65 6d 65 6e | 74 73 2c 20 74 68 6f 75 |e elemen|ts, thou|
|00000140| 67 68 0d 74 68 65 79 20 | 6e 65 65 64 20 6e 6f 74 |gh.they |need not|
|00000150| 20 62 65 20 6f 72 67 61 | 6e 69 73 65 64 20 74 68 | be orga|nised th|
|00000160| 65 20 73 61 6d 65 20 77 | 61 79 2e 20 20 54 68 65 |e same w|ay.  The|
|00000170| 20 72 65 73 75 6c 74 20 | 6f 66 20 74 68 65 20 63 | result |of the c|
|00000180| 72 6f 73 73 0d 70 72 6f | 64 75 63 74 20 69 73 20 |ross.pro|duct is |
|00000190| 72 65 74 75 72 6e 65 64 | 20 61 73 20 61 20 24 31 |returned| as a $1|
|000001a0| 78 33 24 20 6d 61 74 72 | 69 78 2e 0d 0d 24 5c 4c |x3$ matr|ix...$\L|
|000001b0| 6f 6e 67 72 69 67 68 74 | 61 72 72 6f 77 24 20 54 |ongright|arrow$ T|
|000001c0| 68 69 73 20 69 73 20 6e | 6f 74 20 61 6e 20 5c 52 |his is n|ot an \R|
|000001d0| 4c 61 42 5c 20 62 75 69 | 6c 74 2d 69 6e 20 66 75 |LaB\ bui|lt-in fu|
|000001e0| 6e 63 74 69 6f 6e 2e 20 | 20 54 68 69 73 20 66 75 |nction. | This fu|
|000001f0| 6e 63 74 69 6f 6e 0d 69 | 73 20 6e 6f 72 6d 61 6c |nction.i|s normal|
|00000200| 6c 79 20 6c 6f 61 64 65 | 64 20 6f 6e 20 73 74 61 |ly loade|d on sta|
|00000210| 72 74 2d 75 70 20 66 72 | 6f 6d 20 74 68 65 20 5c |rt-up fr|om the \|
|00000220| 76 65 72 62 2b 63 72 6f | 73 73 2e 72 2b 20 66 69 |verb+cro|ss.r+ fi|
|00000230| 6c 65 20 69 6e 20 74 68 | 65 0d 73 74 61 6e 64 61 |le in th|e.standa|
|00000240| 72 64 20 5c 76 65 72 62 | 2b 72 6c 69 62 2b 20 64 |rd \verb|+rlib+ d|
|00000250| 69 72 65 63 74 6f 72 79 | 2e 20 55 73 65 20 6f 66 |irectory|. Use of|
|00000260| 20 74 68 65 20 5c 76 65 | 72 62 2b 2d 72 2b 20 6f | the \ve|rb+-r+ o|
|00000270| 70 74 69 6f 6e 2c 20 69 | 6e 63 6f 72 72 65 63 74 |ption, i|ncorrect|
|00000280| 6c 79 20 0d 73 65 74 74 | 69 6e 67 20 74 68 65 20 |ly .sett|ing the |
|00000290| 5c 76 65 72 62 2b 52 4c | 41 42 5f 4c 49 42 5f 44 |\verb+RL|AB_LIB_D|
|000002a0| 49 52 2b 20 65 6e 76 69 | 72 6f 6e 6d 65 6e 74 61 |IR+ envi|ronmenta|
|000002b0| 6c 20 76 61 72 69 61 62 | 6c 65 2c 20 6f 72 20 6d |l variab|le, or m|
|000002c0| 6f 64 69 66 79 69 6e 67 | 0d 5c 76 65 72 62 2b 63 |odifying|.\verb+c|
|000002d0| 72 6f 73 73 2e 72 2b 20 | 6d 61 79 20 6d 61 6b 65 |ross.r+ |may make|
|000002e0| 20 74 68 69 73 20 66 75 | 6e 63 74 69 6f 6e 20 75 | this fu|nction u|
|000002f0| 6e 61 76 61 69 6c 61 62 | 6c 65 2e 0d 20 0d 5c 70 |navailab|le.. .\p|
|00000300| 61 72 61 67 72 61 70 68 | 7b 45 78 61 6d 70 6c 65 |aragraph|{Example|
|00000310| 7d 0d 5c 69 6e 64 65 78 | 7b 65 78 61 6d 70 6c 65 |}.\index|{example|
|00000320| 20 6f 66 20 63 72 6f 73 | 73 28 29 7d 0d 5c 69 6e | of cros|s()}.\in|
|00000330| 64 65 78 7b 63 72 6f 73 | 73 21 65 78 61 6d 70 6c |dex{cros|s!exampl|
|00000340| 65 7d 0d 5c 62 65 67 69 | 6e 7b 76 65 72 62 61 74 |e}.\begi|n{verbat|
|00000350| 69 6d 7d 0d 3e 20 61 20 | 3d 20 5b 30 2c 30 2c 31 |im}.> a |= [0,0,1|
|00000360| 5d 0d 20 61 20 3d 0d 20 | 20 20 20 20 20 20 20 30 |]. a =. |       0|
|00000370| 20 20 20 20 20 20 20 20 | 20 20 30 20 20 20 20 20 |        |  0     |
|00000380| 20 20 20 20 20 31 20 20 | 0d 3e 20 62 20 3d 20 5b |     1  |.> b = [|
|00000390| 31 3b 30 3b 30 5d 0d 20 | 62 20 3d 0d 20 20 20 20 |1;0;0]. |b =.    |
|000003a0| 20 20 20 20 31 20 20 0d | 20 20 20 20 20 20 20 20 |    1  .|        |
|000003b0| 30 20 20 0d 20 20 20 20 | 20 20 20 20 30 20 20 0d |0  .    |    0  .|
|000003c0| 3e 20 63 20 3d 20 63 72 | 6f 73 73 28 61 2c 62 29 |> c = cr|oss(a,b)|
|000003d0| 0d 20 63 20 3d 0d 20 20 | 20 20 20 20 20 20 30 20 |. c =.  |      0 |
|000003e0| 20 20 20 20 20 20 20 20 | 20 31 20 20 20 20 20 20 |        | 1      |
|000003f0| 20 20 20 20 30 20 20 0d | 3e 20 64 20 3d 20 63 72 |    0  .|> d = cr|
|00000400| 6f 73 73 28 61 2c 63 29 | 0d 20 64 20 3d 0d 20 20 |oss(a,c)|. d =.  |
|00000410| 20 20 20 20 20 2d 31 20 | 20 20 20 20 20 20 20 20 |     -1 |        |
|00000420| 2d 30 20 20 20 20 20 20 | 20 20 20 20 30 20 20 0d |-0      |    0  .|
|00000430| 3e 20 64 20 3d 20 63 72 | 6f 73 73 28 63 2c 61 29 |> d = cr|oss(c,a)|
|00000440| 0d 20 64 20 3d 0d 20 20 | 20 20 20 20 20 20 31 20 |. d =.  |      1 |
|00000450| 20 20 20 20 20 20 20 20 | 2d 30 20 20 20 20 20 20 |        |-0      |
|00000460| 20 20 20 20 30 20 20 0d | 3e 20 65 20 3d 20 5b 31 |    0  .|> e = [1|
|00000470| 2c 31 2c 31 5d 0d 20 65 | 20 3d 0d 20 20 20 20 20 |,1,1]. e| =.     |
|00000480| 20 20 20 31 20 20 20 20 | 20 20 20 20 20 20 31 20 |   1    |      1 |
|00000490| 20 20 20 20 20 20 20 20 | 20 31 20 20 0d 3e 20 63 |        | 1  .> c|
|000004a0| 72 6f 73 73 28 61 2c 65 | 29 0d 20 20 20 20 20 20 |ross(a,e|).      |
|000004b0| 20 2d 31 20 20 20 20 20 | 20 20 20 20 20 31 20 20 | -1     |     1  |
|000004c0| 20 20 20 20 20 20 20 20 | 30 20 20 0d 3e 20 63 72 |        |0  .> cr|
|000004d0| 6f 73 73 28 63 2c 65 29 | 0d 20 20 20 20 20 20 20 |oss(c,e)|.       |
|000004e0| 20 31 20 20 20 20 20 20 | 20 20 20 2d 30 20 20 20 | 1      |   -0   |
|000004f0| 20 20 20 20 20 20 2d 31 | 20 20 0d 5c 65 6e 64 7b |      -1|  .\end{|
|00000500| 76 65 72 62 61 74 69 6d | 7d 0d 0d 53 65 65 20 61 |verbatim|}..See a|
|00000510| 6c 73 6f 3a 20 50 61 67 | 65 7e 5c 70 61 67 65 72 |lso: Pag|e~\pager|
|00000520| 65 66 7b 66 6e 3a 64 6f | 74 7d 20 5c 76 65 72 62 |ef{fn:do|t} \verb|
|00000530| 2b 64 6f 74 28 29 2b 2e | 0d 0d 5c 6e 65 77 70 61 |+dot()+.|..\newpa|
|00000540| 67 65 0d 0d 0d 0d 0d 0d | 0d                      |ge......|.       |
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